arXiv research

Neural Diffusion Intensity Models simplify Cox processes inference.

A new method clusters rows of a matrix of point processes.

Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions that do not have a closed form or that are restricted to specific covariance funct…

Paper extends multi-task Gaussian Cox processes for heterogeneous tasks.

Bayesian approach for inhomogeneous Poisson process intensity estimation.

The paper develops methods to create private synthetic spatial point patterns.

We consider the intensity-based approach for the modeling of default times of one or more companies. In this approach the default times are defined as the jump times of a Cox process, which is a Poisson process conditional on the realization of its intensity. We assume that the intensity follows the Cox-Ingersoll-Ross …

Study adaptive sensing of Cox processes using posterior sampling and positive bases.

We generalize the log Gaussian Cox process (LGCP) framework to model multiple correlated point data jointly. The observations are treated as realizations of multiple LGCPs, whose log intensities are given by linear combinations of latent functions drawn from Gaussian process priors. The combination coefficients are als…

We study convergence properties of the full truncation Euler scheme for the Cox-Ingersoll-Ross process in the regime where the boundary point zero is inaccessible. Under some conditions on the model parameters (precisely, when the Feller ratio is greater than three), we establish the strong order 1/2 convergence in $L^…

Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few thousand data points. Here we introduce Cox process inference based on Fourier feat…

This paper presents a Bayesian generative model for dependent Cox point processes, alongside an efficient inference scheme which scales as if the point processes were modelled independently. We can handle missing data naturally, infer latent structure, and cope with large numbers of observed processes. A further novel …

Study on Volterra Cox-Ingersoll-Ross process, proving asymptotic independence and ergodicity.

In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result, the arrival process can be dependent, non-stationary and non-renewal. We give t…

McCullagh and Yang (2006) suggest a family of classification algorithms based on Cox processes. We further investigate the log Gaussian variant which has a number of appealing properties. Conditioned on the covariates, the distribution over labels is given by a type of conditional Markov random field. In the supervised…

New Hawkes processes model spatiotemporal events with triggering and clustering.

Modeling dependent defaults with multivariate Cox processes.

Defines a new process for financial modeling.

SurvLIME explains survival models by approximating them with Cox models.

During the past decades, the Ising distribution has attracted interest in many applied disciplines, as the maximum entropy distribution associated to any set of correlated binary (`spin') variables with observed means and covariances. However, numerically speaking, the Ising distribution is unpractical, so alternative …

A deep Neyman-Scott process uses Poisson processes for efficient inference in complex point processes.

Develops a method to model multivariate count processes with Cox processes and shot noise intensities.

Study explains mortgage burnout using Cox hazard models.

New high-order approximations for CIR process using random grids.

We analyze exponential integrability properties of the Cox-Ingersoll-Ross (CIR) process and its Euler discretizations with various types of truncation and reflection at 0. These properties play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a class of sto…

Study sharp convergence rates of empirical UOT for spatio-temporal point processes.

Paper introduces a new model for cyber insurance pricing.

This paper studies the critical dynamics of random surfaces, focusing on area and genus evolution.

New financial price model using earning yield derived from CIR process.

Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling generally required and the analytically intractable likelihood function. Here, we expl…

The Bivariate Dynamic Contagion Processes (BDCP) are a broad class of bivariate point processes characterized by the intensities as a general class of piecewise deterministic Markov processes. The BDCP describes a rich dynamic structure where the system is under the influence of both external and internal factors model…

We present a non-parametric prognostic framework for individualized event prediction based on joint modeling of both longitudinal and time-to-event data. Our approach exploits a multivariate Gaussian convolution process (MGCP) to model the evolution of longitudinal signals and a Cox model to map time-to-event data with…

A new adaptive splitting method improves accuracy for Cox-Ingersoll-Ross model.

DPP-BBO diversifies batched Bayesian optimization using DPPs.

The variational framework for learning inducing variables (Titsias, 2009a) has had a large impact on the Gaussian process literature. The framework may be interpreted as minimizing a rigorously defined Kullback-Leibler divergence between the approximating and posterior processes. To our knowledge this connection has th…

We propose a scalable framework for inference in an inhomogeneous Poisson process modeled by a continuous sigmoidal Cox process that assumes the corresponding intensity function is given by a Gaussian process (GP) prior transformed with a scaled logistic sigmoid function. We present a tractable representation of the li…

Developing a climate-aware pricing framework for XL reinsurance and CAT bonds under non-stationary catastrophe risk.

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate…

We investigate the asymptotic behavior as time goes to infinity of Hawkes processes whose regression kernel has $L^1$ norm close to one and power law tail of the form $x^{-(1+α)}$, with $α\in(0,1)$. We in particular prove that when $α\in(1/2,1)$, after suitable rescaling, their law converges to that of a kind of integr…

We discover subgroups for Cox model survival analysis, improving model accuracy.

In common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his continuous-time consumption-portfolio problem, deriving general equilibrium relationships …

Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity functions exist, especially when observed points lie in a high-dimensional space.…

Two methods improve simulation of European call options under Heston model.

A new method for automatic gradient tree boosting using information theory.

New statistical properties for mini-batch Cox-NN optimization.

Study on non-negative solutions for stochastic Volterra equations with jumps.

We introduce the binacox, a prognostic method to deal with the problem of detecting multiple cut-points per features in a multivariate setting where a large number of continuous features are available. The method is based on the Cox model and combines one-hot encoding with the binarsity penalty, which uses total-variat…

Active-set algorithm improves Cox regression for shape-restricted covariates.